Philipp Reinhard Vitriarius was born in Oppenheim on 17 February 1647. He studied law at the University of Strassburg under Johann Heinrich Boecler. He obtained his doctoral degree on 11 December 1672 with his Theses Inaugurales Juridicae de Iure antecessoris in successorem. In 1675 he was appointed honorary professor of law at the Academy of Geneva, as successor of André Weguelin. He became full professor (salaried) in 1677. On 25 September 1682 he was appointed professor of German public law at Leiden University. He succeeded Johannes Friedrich Böckelmann on this chair. Due to ill health, he resigned on 21 October 1719 in favour of his son Johann Jacob Vitriarius. He attracted a great number of German students, especially from Austria.

We do not know whether Vitriarius taught the law of nature and nations while he was professor at the Academy of Geneva. This might be the case given that he published in 1692 his Institutiones iuris naturae et gentium in usum serenissimi principis Ludovici Marchionis brandenburgici [...] ad methodum Hugonis Grotii. This work was edited many times. A new edition with notes by D. L. Vullyamozius was published in Lausanne in 1745. Vitriarius was however better known for his Institutiones iuris publici Romano-Germanici, first published in Speier under the pseudonym Nicolaus Danckwerths and with a different title, and in the same year under his real name in Frankfurt. This and later editions were accompanied by the commentaries of Johann Friedrich Pfeffinger (1667-1730), that is, excerpts from various sources entitled "Vitriarius illustratus".